关于正规算子、其指数算子族及对称算子的非超循环性
On the non-hypercyclicity of normal operators, collections of their exponentials, and symmetric operators
California State University, Fresno（弗雷斯诺州立大学）
AI总结：
该研究针对复希尔伯特空间中的正规算子、其指数算子族及对称算子，给出了它们非超循环性的简单直接证明，补充了对称算子非超循环性的相关结论。
摘要：
我们给出复希尔伯特空间中任意正规算子A（有界或无界）及其指数算子族{e^{tA}}_{t≥0}的非超循环性的简单直接证明，当A的谱满足一定条件时，该指数算子族是A生成的C0半群；同时证明了对称算子的非超循环性。
英文摘要：
We give a simple, straightforward proof of the non-hypercyclicity of an arbitrary normal operator $A$ (bounded or unbounded) in a complex Hilbert space as well as of the collection $\left\{e^{tA}\right\}_{t\ge 0}$ of its exponentials, which, under a certain condition on the spectrum of $A$, is the $C_0$-semigroup generated by it. We also establish non-hypercyclicity for symmetric operators.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
